{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T03:11:32Z","timestamp":1777086692068,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2021,11,20]],"date-time":"2021-11-20T00:00:00Z","timestamp":1637366400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In general, for the configuration designs of underwater robots, the positions and directions of actuators (i.e., thrusters) are given and installed in conventional ways (known points, vertically, horizontally). This yields limitations for the capability of robots and does not optimize the robot\u2019s resources such as energy, reactivity, and versatility, especially when the robots operate in confined environments. In order to optimize the configuration designs in the underwater robot field focusing on over-actuated systems, in the paper, performance indices (manipulability, energetic, reactive, and robustness indices) are introduced. The multi-objective optimization problem was formulated and analyzed. To deal with different objectives with different units, the goal-attainment method, which can avoid the difficulty of choosing a weighting vector to obtain a good balance among these objectives, was selected to solve the problem. A solution design procedure is proposed and discussed. The efficiency of the proposed method was proven by simulations and experimental results.<\/jats:p>","DOI":"10.3390\/s21227729","type":"journal-article","created":{"date-parts":[[2021,11,21]],"date-time":"2021-11-21T21:00:50Z","timestamp":1637528450000},"page":"7729","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Over-Actuated Underwater Robots: Configuration Matrix Design and Perspectives"],"prefix":"10.3390","volume":"21","author":[{"given":"Tho","family":"Dang","sequence":"first","affiliation":[{"name":"Laboratory of Informatics, Robotics and MicroElectronics (LIRMM) (UMR 5506 CNRS\u2014UM), Universit\u00e9 Montpellier, 161 rue Ada, CEDEX 5, 34392 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4320-2118","authenticated-orcid":false,"given":"Lionel","family":"Lapierre","sequence":"additional","affiliation":[{"name":"Laboratory of Informatics, Robotics and MicroElectronics (LIRMM) (UMR 5506 CNRS\u2014UM), Universit\u00e9 Montpellier, 161 rue Ada, CEDEX 5, 34392 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rene","family":"Zapata","sequence":"additional","affiliation":[{"name":"Laboratory of Informatics, Robotics and MicroElectronics (LIRMM) (UMR 5506 CNRS\u2014UM), Universit\u00e9 Montpellier, 161 rue Ada, CEDEX 5, 34392 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benoit","family":"Ropars","sequence":"additional","affiliation":[{"name":"Reeds Company, 199 rue H\u00e9l\u00e8ne Boucher, 34170 Castelnau-Le-Lez, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pascal","family":"Lepinay","sequence":"additional","affiliation":[{"name":"Laboratory of Informatics, Robotics and MicroElectronics (LIRMM) (UMR 5506 CNRS\u2014UM), Universit\u00e9 Montpellier, 161 rue Ada, CEDEX 5, 34392 Montpellier, France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.oceaneng.2008.10.006","article-title":"Robust diving control of an AUV","volume":"36","author":"Lapierre","year":"2009","journal-title":"Ocean Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1109\/JOE.2008.923554","article-title":"Robust nonlinear path-following control of an AUV","volume":"33","author":"Lapierre","year":"2008","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_3","unstructured":"Levine, W.S. (2010). The Control Systems Handbook: Control System Applications, CRC Press."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1016\/j.automatica.2013.01.035","article-title":"Control allocation\u2014A survey","volume":"49","author":"Johansen","year":"2013","journal-title":"Automatica"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1016\/j.oceaneng.2017.12.025","article-title":"Redundant actuation system of an underwater vehicle","volume":"151","author":"Ropars","year":"2018","journal-title":"Ocean Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498700600201","article-title":"Task-priority based redundancy control of robot manipulators","volume":"6","author":"Nakamura","year":"1987","journal-title":"Int. J. Robot. Res."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Adorno, B.V., Fraisse, P., and Druon, S. (2010, January 18\u201322). Dual position control strategies using the cooperative dual task-space framework. Proceedings of the IROS\u201910: International Conference on Intelligent Robots and Systems, Taipei, Taiwan.","DOI":"10.1109\/IROS.2010.5650218"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Agravante, D.J., Sherikov, A., Wieber, P.B., Cherubini, A., and Kheddar, A. (2016, January 16\u201321). Walking pattern generators designed for physical collaboration. Proceedings of the ICRA 2016: 2016 IEEE International Conference on Robotics and Automation (ICRA), Stockholm, Sweden.","DOI":"10.1109\/ICRA.2016.7487296"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2343","DOI":"10.1109\/TII.2017.2760912","article-title":"Multicontact Interaction Force Sensing From Whole-Body Motion Capture","volume":"14","author":"Pham","year":"2018","journal-title":"IEEE Trans. Ind. Inform."},{"key":"ref_10","unstructured":"Yoshikawa, T. (1985, January 25\u201328). Dynamic manipulability of robot manipulators. Proceedings of the 1985 IEEE International Conference on Robotics and Automation, St. Louis, MO, USA."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Yoshikawa, T. (1990). Foundations of Robotics: Analysis and Control, MIT Press.","DOI":"10.7551\/mitpress\/3074.001.0001"},{"key":"ref_12","first-page":"665","article-title":"The workspaces of a mechanical manipulator","volume":"103","author":"Kumar","year":"1981","journal-title":"J. Mech. Des."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1177\/027836498800700204","article-title":"Optimal kinematic design of 6R manipulators","volume":"7","author":"Paden","year":"1988","journal-title":"Int. J. Robot. Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1177\/027836499401300101","article-title":"Kinematic dexterity of robotic mechanisms","volume":"13","author":"Park","year":"1994","journal-title":"Int. J. Robot. Res."},{"key":"ref_15","unstructured":"Pierrot, F., Benoit, M., and Dauchez, P. (October, January 28). Optimal thruster configuration for omni-directional underwater vehicles. SamoS: A Pythagorean solution. Proceedings of the OCEANS \u201998 Conference Proceedings, Nice, France."},{"key":"ref_16","unstructured":"Kharrat, H. (2015). Optimization of Thruster Configuration for Swimming Robots. [Master\u2019s Thesis, Rice University]."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/TCST.2017.2765622","article-title":"Fast Exact Redistributed Pseudoinverse Method for Linear Actuation Systems","volume":"27","author":"Stephan","year":"2017","journal-title":"IEEE Trans. Control Syst. Technol."},{"key":"ref_18","unstructured":"Grechi, S., and Caiti, A. (2016, January 13\u201316). Comparison between Optimal Control Allocation with Mixed Quadratic & Linear Programming Techniques. Proceedings of the 10th IFAC Conference on Control Applications in Marine SystemsCAMS, Trondheim, Norway."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ropars, B., Lasbouygues, A., Lapierre, L., and Andreu, D. (2015, January 15\u201317). Thruster\u2019s dead-zones compensation for the actuation system of an underwater vehicle. Proceedings of the Control Conference (ECC), Linz, Austria.","DOI":"10.1109\/ECC.2015.7330631"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1177\/027836498500400201","article-title":"Manipulability of robotic mechanisms","volume":"4","author":"Yoshikawa","year":"1985","journal-title":"Int. J. Robot. Res."},{"key":"ref_21","unstructured":"Olver, F.W., Lozier, D.W., Boisvert, R.F., and Clark, C.W. (2010). NIST Handbook of Mathematical Functions Hardback and CD-ROM, Cambridge University Press."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Trefethen, L.N., and Bau, D. (1997). Numerical Linear Algebra, Siam.","DOI":"10.1137\/1.9780898719574"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1109\/TAC.1975.1101105","article-title":"Approach to performance and sensitivity multiobjective optimization: The goal-attainment method","volume":"20","author":"Gembicki","year":"1975","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_24","unstructured":"(2018, December 20). BlueRobotics. Available online: https:\/\/bluerobotics.com\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7729\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:33:15Z","timestamp":1760167995000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/22\/7729"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,20]]},"references-count":24,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2021,11]]}},"alternative-id":["s21227729"],"URL":"https:\/\/doi.org\/10.3390\/s21227729","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,20]]}}}